Question

Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn = ((xn−1)+(xn−2))/...

Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn = ((xn−1)+(xn−2))/ 2 for n > 2. Prove that limn→∞ xn = x exists and find its value.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1)...
Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1) for n > 0. Prove that limn→∞ xn = x exists and find its value.
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2....
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2. Prove that Xn=O(2.4^n) and Xn = Ω(2.3^n). Hint:First, prove by induction that 1/2*(2.3^n) ≤ Xn ≤ 2.8^n for all n ≥ 0 Find claim, base case and inductive step. Please show step and explain all work and details
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that...
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that lim n→∞ (x1 + x2 + · · · + xn)/ n = 0 .
Consider the sequence (xn)n given by x1 = 2, x2 = 2 and xn+1 = 2(xn...
Consider the sequence (xn)n given by x1 = 2, x2 = 2 and xn+1 = 2(xn + xn−1). (a) Let u, w be the solutions of the equation x 2 −2x−2 = 0, so that x 2 −2x−2 = (x−u)(x−w). Show that u + w = 2 and uw = −2. (b) Possibly using (a) to aid your calculations, show that xn = u^n + w^n .
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 +...
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 + x2 + · · · + xn = 1. Prove that √ x1 + √ x2 + · · · + √ xn /√ n − 1 ≤ x1/ √ 1 − x1 + x2/ √ 1 − x2 + · · · + xn/ √ 1 − xn
) Let α be a fixed positive real number, α > 0. For a sequence {xn},...
) Let α be a fixed positive real number, α > 0. For a sequence {xn}, let x1 > √ α, and define x2, x3, x4, · · · by the following recurrence relation xn+1 = 1 2 xn + α xn (a) Prove that {xn} decreases monotonically (in other words, xn+1 − xn ≤ 0 for all n). (b) Prove that {xn} is bounded from below. (Hint: use proof by induction to show xn > √ α for all...
Let xn be a sequence such that for every m ∈ N, m ≥ 2 the...
Let xn be a sequence such that for every m ∈ N, m ≥ 2 the sequence limn→∞ xmn = L. Prove or provide a counterexample: limn→∞ xn = L.
Define a Q-sequence recursively as follows. B.   x, 4 − x is a Q-sequence for any...
Define a Q-sequence recursively as follows. B.   x, 4 − x is a Q-sequence for any real number x. R.   If x1, x2,   , xj and y1, y2,   , yk are Q-sequences, so is     x1 − 1, x2,   , xj, y1, y2,   , yk − 3. Use structural induction (i.e., induction on the recursive definition) to prove that the sum of the numbers in any Q-sequence is 4. Base Case: Any Q-sequence formed by the base case of the definition has sum x +...
If (xn) is a sequence of nonzero real numbers and if limn→∞ xn = x where...
If (xn) is a sequence of nonzero real numbers and if limn→∞ xn = x where x does not equal zero; prove that lim n→∞ 1/ xn = 1/x
X1,X2, . . . is a sequence of iid Bernoulli (1/2) random variables. Consider the random...
X1,X2, . . . is a sequence of iid Bernoulli (1/2) random variables. Consider the random sequence Y_n = X_1 +· · ·+X_n. (a) What is limn→∞ P[|Y_2n − n| ≤ (n/2)^1/2? (b) What does the weak law of large numbers say about Y2n? Could I get a little clarification with this problem?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT